Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?

Saying that someone is a chaotic thinker might seem like an insult - but, according to Lewis Dartnell, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work.

During the Second World War, the Allies' codebreakers worked at Bletchley Park to decipher the supposedly unbreakable Enigma code. Claire Ellis tells us about their heroic efforts, which historians believe shortened the war by two years.

Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.

There are problems that are easy to solve in theory, but impossible to solve in practice. Intrigued? Then join us on a journey through the world of complexity, all the way to the famous P versus NP conjecture.